Barros, Carlos Filipe (2010) On the Lebesgue-Nagell equation and related subjects. PhD thesis, University of Warwick.

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Abstract

The work of Cohn [Coh93] and Bugeaud, Mignotte and Siksek [BMS06] solves
the Lebesgue-Naguel equation
x2 + D = yn, x, y integers, n ≥ 3
for D a integer in the range 1 ≤ D ≤ 100. We propose to do the same for D
in the range -100 ≤ D ≤ -1. For that we will use techniques that go from the
most classical ones, ideal factorization over number fields and Thue equations, to
the most modern approach to Diophantine equations, Frey curves and the Modular
approach, passing by linear forms in logarithms.

Item Type:	Thesis (PhD)
Subjects:	Q Science > QA Mathematics
Library of Congress Subject Headings (LCSH):	Number theory, Factorization (Mathematics)
Official Date:	August 2010
Dates:	Date Event August 2010 Submitted
Institution:	University of Warwick
Theses Department:	Mathematics Institute
Thesis Type:	PhD
Publication Status:	Unpublished
Supervisor(s)/Advisor:	Siksek, Samir
Sponsors:	Fundação para a Ciência e a Tecnologia (FCT) (SFRH/BD/29433/2006)
Extent:	xiii, 292 leaves
Language:	eng

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